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Sudoku for Beginners: How to Improve Your Problem-Solving Skills

Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

Understanding the Basics of Sudoku

Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.

Starting Strategies for Beginners

As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.

Advanced Strategies for Beginner/Intermediate Level

Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.

Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.

Benefits of Solving Sudoku Puzzles

Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.

In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.

This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.

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How to Solve Coding Problems with a Simple Four Step Method

I had fifteen minutes left, and I knew I was going to fail.

I had spent two months studying for my first technical interview.

I thought I was prepared, but as the interview came to a close, it hit me: I had no idea how to solve coding problems.

Of all the tutorials I had taken when I was learning to code, not one of them had included an approach to solving coding problems.

I had to find a method for problem-solving—my career as a developer depended on it.

I immediately began researching methods. And I found one. In fact, what I uncovered was an invaluable strategy. It was a time-tested four-step method that was somehow under the radar in the developer ecosystem.

In this article, I’ll go over this four-step problem-solving method that you can use to start confidently solving coding problems.

Solving coding problems is not only part of the developer job interview process—it’s what a developer does all day. After all, writing code is problem-solving.

A method for solving problems

This method is from the book How to Solve It by George Pólya. It originally came out in 1945 and has sold over one million copies.

His problem-solving method has been used and taught by many programmers, from computer science professors (see Udacity’s Intro to CS course taught by professor David Evans) to modern web development teachers like Colt Steele.

Let’s walk through solving a simple coding problem using the four-step problem-solving method. This allows us to see the method in action as we learn it. We'll use JavaScript as our language of choice. Here’s the problem:

Create a function that adds together two numbers and returns that value. There are four steps to the problem-solving method:

• Understand the problem.
• Devise a plan.
• Carry out the plan.

Let’s get started with step one.

Step 1: Understand the problem.

When given a coding problem in an interview, it’s tempting to rush into coding. This is hard to avoid, especially if you have a time limit.

However, try to resist this urge. Make sure you actually understand the problem before you get started with solving it.

Read through the problem. If you’re in an interview, you could read through the problem out loud if that helps you slow down.

As you read through the problem, clarify any part of it you do not understand. If you’re in an interview, you can do this by asking your interviewer questions about the problem description. If you’re on your own, think through and/or Google parts of the question you might not understand.

This first step is vital as we often don’t take the time to fully understand the problem. When you don’t fully understand the problem, you’ll have a much harder time solving it.

To help you better understand the problem, ask yourself:

What are the inputs?

What kinds of inputs will go into this problem? In this example, the inputs are the arguments that our function will take.

Just from reading the problem description so far, we know that the inputs will be numbers. But to be more specific about what the inputs will be, we can ask:

Will the inputs always be just two numbers? What should happen if our function receives as input three numbers?

Here we could ask the interviewer for clarification, or look at the problem description further.

The coding problem might have a note saying, “You should only ever expect two inputs into the function.” If so, you know how to proceed. You can get more specific, as you’ll likely realize that you need to ask more questions on what kinds of inputs you might be receiving.

Will the inputs always be numbers? What should our function do if we receive the inputs “a” and “b”? Clarify whether or not our function will always take in numbers.

Optionally, you could write down possible inputs in a code comment to get a sense of what they’ll look like:

//inputs: 2, 4

What are the outputs?

What will this function return? In this case, the output will be one number that is the result of the two number inputs. Make sure you understand what your outputs will be.

Create some examples.

Once you have a grasp of the problem and know the possible inputs and outputs, you can start working on some concrete examples.

Examples can also be used as sanity checks to test your eventual problem. Most code challenge editors that you’ll work in (whether it’s in an interview or just using a site like Codewars or HackerRank) have examples or test cases already written for you. Even so, writing out your own examples can help you cement your understanding of the problem.

Start with a simple example or two of possible inputs and outputs. Let's return to our addition function.

Let’s call our function “add.”

What’s an example input? Example input might be:

// add(2, 3)

What is the output to this? To write the example output, we can write:

// add(2, 3) ---> 5

This indicates that our function will take in an input of 2 and 3 and return 5 as its output.

Create complex examples.

By walking through more complex examples, you can take the time to look for edge cases you might need to account for.

For example, what should we do if our inputs are strings instead of numbers? What if we have as input two strings, for example, add('a', 'b')?

Your interviewer might possibly tell you to return an error message if there are any inputs that are not numbers. If so, you can add a code comment to handle this case if it helps you remember you need to do this.

Your interviewer might also tell you to assume that your inputs will always be numbers, in which case you don’t need to write any extra code to handle this particular input edge case.

If you don’t have an interviewer and you’re just solving this problem, the problem might say what happens when you enter invalid inputs.

For example, some problems will say, “If there are zero inputs, return undefined.” For cases like this, you can optionally write a comment.

// check if there are no inputs.

// If no inputs, return undefined.

For our purposes, we’ll assume that our inputs will always be numbers. But generally, it’s good to think about edge cases.

Computer science professor Evans says to write what developers call defensive code. Think about what could go wrong and how your code could defend against possible errors.  

Before we move on to step 2, let’s summarize step 1, understand the problem:

-Read through the problem.

-What are the inputs?

-What are the outputs?

Create simple examples, then create more complex ones.

2. Devise a plan for solving the problem.

Next, devise a plan for how you’ll solve the problem. As you devise a plan, write it out in pseudocode.

Pseudocode is a plain language description of the steps in an algorithm. In other words, your pseudocode is your step-by-step plan for how to solve the problem.

Write out the steps you need to take to solve the problem. For a more complicated problem, you’d have more steps. For this problem, you could write:

// Create a sum variable.

Add the first input to the second input using the addition operator .

// Store value of both inputs into sum variable.

// Return as output the sum variable. Now you have your step-by-step plan to solve the problem. For more complex problems, professor Evans notes, “Consider systematically how a human solves the problem.” That is, forget about how your code might solve the problem for a moment, and think about how you would solve it as a human. This can help you see the steps more clearly.

3. Carry out the plan (Solve the problem!)

The next step in the problem-solving strategy is to solve the problem. Using your pseudocode as your guide, write out your actual code.

Professor Evans suggests focusing on a simple, mechanical solution. The easier and simpler your solution is, the more likely you can program it correctly.

Taking our pseudocode, we could now write this:

Professor Evans adds, remember not to prematurely optimize. That is, you might be tempted to start saying, “Wait, I’m doing this and it’s going to be inefficient code!”

First, just get out your simple, mechanical solution.

What if you can’t solve the entire problem? What if there's a part of it you still don't know how to solve?

Colt Steele gives great advice here: If you can’t solve part of the problem, ignore that hard part that’s tripping you up. Instead, focus on everything else that you can start writing.

Temporarily ignore that difficult part of the problem you don’t quite understand and write out the other parts. Once this is done, come back to the harder part.

This allows you to get at least some of the problem finished. And often, you’ll realize how to tackle that harder part of the problem once you come back to it.

Step 4: Look back over what you've done.

Once your solution is working, take the time to reflect on it and figure out how to make improvements. This might be the time you refactor your solution into a more efficient one.

As you look at your work, here are some questions Colt Steele suggests you ask yourself to figure out how you can improve your solution:

• Can you derive the result differently? What other approaches are there that are viable?
• Can you understand it at a glance? Does it make sense?
• Can you use the result or method for some other problem?
• Can you improve the performance of your solution?
• Can you think of other ways to refactor?
• How have other people solved this problem?

One way we might refactor our problem to make our code more concise: removing our variable and using an implicit return:

With step 4, your problem might never feel finished. Even great developers still write code that they later look at and want to change. These are guiding questions that can help you.

If you still have time in an interview, you can go through this step and make your solution better. If you are coding on your own, take the time to go over these steps.

When I’m practicing coding on my own, I almost always look at the solutions out there that are more elegant or effective than what I’ve come up with.

Wrapping Up

In this post, we’ve gone over the four-step problem-solving strategy for solving coding problems.

Let's review them here:

• Step 1: understand the problem.
• Step 2: create a step-by-step plan for how you’ll solve it .
• Step 3: carry out the plan and write the actual code.
• Step 4: look back and possibly refactor your solution if it could be better.

Practicing this problem-solving method has immensely helped me in my technical interviews and in my job as a developer. If you don't feel confident when it comes to solving coding problems, just remember that problem-solving is a skill that anyone can get better at with time and practice.

If you enjoyed this post, join my coding club , where we tackle coding challenges together every Sunday and support each other as we learn new technologies.

If you have feedback or questions on this post, feel free to tweet me @madisonkanna ..

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Lesson 27 of 33 By Hemant Deshpande

Table of Contents

Coding and Programming skills hold a significant and critical role in implementing and developing various technologies and software. They add more value to the future and development. These programming and coding skills are essential for every person to improve problem solving skills. So, we brought you this article to help you learn and know the importance of these skills in the future. 

Basics to Advanced - Learn It All!

Topics covered in this problem solving in programming article are:

• What is Problem Solving in Programming? 
• Problem Solving skills in Programming
• How does it impact your career ?
• Steps involved in Problem Solving
• Steps to improve Problem Solving in programming

What is Problem Solving in Programming?

Computers are used to solve various problems in day-to-day life. Problem Solving is an essential skill that helps to solve problems in programming. There are specific steps to be carried out to solve problems in computer programming, and the success depends on how correctly and precisely we define a problem. This involves designing, identifying and implementing problems using certain steps to develop a computer.

When we know what exactly problem solving in programming is, let us learn how it impacts your career growth.

How Does It Impact Your Career?

Many companies look for candidates with excellent problem solving skills. These skills help people manage the work and make candidates put more effort into the work, which results in finding solutions for complex problems in unexpected situations. These skills also help to identify quick solutions when they arise and are identified. 

People with great problem solving skills also possess more thinking and analytical skills, which makes them much more successful and confident in their career and able to work in any kind of environment. 

The above section gives you an idea of how problem solving in programming impacts your career and growth. Now, let's understand what problem solving skills mean.

Problem Solving Skills in Programming

Solving a question that is related to computers is more complicated than finding the solutions for other questions. It requires excellent knowledge and much thinking power. Problem solving in programming skills is much needed for a person and holds a major advantage. For every question, there are specific steps to be followed to get a perfect solution. By using those steps, it is possible to find a solution quickly.

The above section is covered with an explanation of problem solving in programming skills. Now let's learn some steps involved in problem solving.

Steps Involved in Problem Solving

Before being ready to solve a problem, there are some steps and procedures to be followed to find the solution. Let's have a look at them in this problem solving in programming article.

Basically, they are divided into four categories:

• Analysing the problem
• Developing the algorithm
• Testing and debugging

Analysing the Problem

Every problem has a perfect solution; before we are ready to solve a problem, we must look over the question and understand it. When we know the question, it is easy to find the solution for it. If we are not ready with what we have to solve, then we end up with the question and cannot find the answer as expected. By analysing it, we can figure out the outputs and inputs to be carried out. Thus, when we analyse and are ready with the list, it is easy and helps us find the solution easily. 

Developing the Algorithm

It is required to decide a solution before writing a program. The procedure of representing the solution  in a natural language called an algorithm. We must design, develop and decide the final approach after a number of trials and errors, before actually writing the final code on an algorithm before we write the code. It captures and refines all the aspects of the desired solution.

Once we finalise the algorithm, we must convert the decided algorithm into a code or program using a dedicated programming language that is understandable by the computer to find a desired solution. In this stage, a wide variety of programming languages are used to convert the algorithm into code. 

Testing and Debugging

The designed and developed program undergoes several rigorous tests based on various real-time parameters and the program undergoes various levels of simulations. It must meet the user's requirements, which have to respond with the required time. It should generate all expected outputs to all the possible inputs. The program should also undergo bug fixing and all possible exception handling. If it fails to show the possible results, it should be checked for logical errors.

Industries follow some testing methods like system testing, component testing and acceptance testing while developing complex applications. The errors identified while testing are debugged or rectified and tested again until all errors are removed from the program.

The steps mentioned above are involved in problem solving in programming. Now let's see some more detailed information about the steps to improve problem solving in programming.

Steps to Improve Problem Solving in Programming

Right mindset.

The way to approach problems is the key to improving the skills. To find a solution, a positive mindset helps to solve problems quickly. If you think something is impossible, then it is hard to achieve. When you feel free and focus with a positive attitude, even complex problems will have a perfect solution.

Making Right Decisions

When we need to solve a problem, we must be clear with the solution. The perfect solution helps to get success in a shorter period. Making the right decisions in the right situation helps to find the perfect solution quickly and efficiently. These skills also help to get more command over the subject.

Keeping Ideas on Track

Ideas always help much in improving the skills; they also help to gain more knowledge and more command over things. In problem solving situations, these ideas help much and help to develop more skills. Give opportunities for the mind and keep on noting the ideas.

Learning from Feedbacks

A crucial part of learning is from the feedback. Mistakes help you to gain more knowledge and have much growth. When you have a solution for a problem, go for the feedback from the experienced or the professionals. It helps you get success within a shorter period and enables you to find other solutions easily.

Here's How to Land a Top Software Developer Job

Asking Questions

Questions are an incredible part of life. While searching for solutions, there are a lot of questions that arise in our minds. Once you know the question correctly, then you are able to find answers quickly. In coding or programming, we must have a clear idea about the problem. Then, you can find the perfect solution for it. Raising questions can help to understand the problem.

These are a few reasons and tips to improve problem solving in programming skills. Now let's see some major benefits in this article.

• Problem solving in programming skills helps to gain more knowledge over coding and programming, which is a major benefit.
• These problem solving skills also help to develop more skills in a person and build a promising career.
• These skills also help to find the solutions for critical and complex problems in a perfect way.
• Learning and developing problem solving in programming helps in building a good foundation.
• Most of the companies are looking for people with good problem solving skills, and these play an important role when it comes to job opportunities 

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Problem solving in programming skills is important in this modern world; these skills build a great career and hold a great advantage. This article on problem solving in programming provides you with an idea of how it plays a massive role in the present world. In this problem solving in programming article, the skills and the ways to improve more command on problem solving in programming are mentioned and explained in a proper way.

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If you have any questions for us on the problem solving in programming article. Do let us know in the comments section below; we have our experts answer it right away.

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About the author.

Hemant Deshpande, PMP has more than 17 years of experience working for various global MNC's. He has more than 10 years of experience in managing large transformation programs for Fortune 500 clients across verticals such as Banking, Finance, Insurance, Healthcare, Telecom and others. During his career he has worked across the geographies - North America, Europe, Middle East, and Asia Pacific. Hemant is an internationally Certified Executive Coach (CCA/ICF Approved) working with corporate leaders. He also provides Management Consulting and Training services. He is passionate about writing and regularly blogs and writes content for top websites. His motto in life - Making a positive difference.

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How to Solve Programming Problems

Written By John Sonmez

Right before the holidays, I said that you had better learn how to solve programming problems .

This time I am going to try and give you some good tools to enable you to get good at solving programming problems.  (Really algorithm type problems specifically.)

Common mistakes

When most programmers are given a programming problem in an interview, they make several key mistakes.  The most severe of those is the improper allocation of time.

If you have heard the saying “measure twice and cut once,” then you are probably familiar with the idea of spending upfront time to make sure something is done right, rather than diving right in.

The most common mistake I see when conducting interviews or watching someone try to solve a programming problem is they try to start writing code as soon as possible.

You must resist this urge.

You really want to make sure you take enough time to understand the problem completely before attempting to solve it.

Another big mistake is trying to over solve the solution on the first iteration.  Keep it simple, don’t try to get fancy.

A simple set of steps

I am going to give you a simple set of steps to follow which you can use for any algorithm type programming problem.

• Read the problem completely twice.
• Solve the problem manually with 3 sets of sample data.
• Optimize the manual steps.
• Write the manual steps as comments or pseudo-code.
• Replace the comments or pseudo-code with real code.
• Optimize the real code.

As much as 70% of our time should be spent in steps 1-3.

Let’s look at each step.

Read the problem completely twice

This is the single most important step.  You may even want to read the problem 3 or 4 times.

You want to make sure you completely understand the problem.  A good test of this is whether or not you can explain the problem to someone else.

I cannot over-emphasize how important this step is!

If you don’t understand the problem, you cannot solve it.  Do not worry about wasting time here, because the better you understand the problem, the easier it will be to solve it.

If you are given any examples along with the problem, make sure you have worked through the examples and understand why the answers are correct for each one.

Solve the problem manually

“Nothing can be automated that cannot be done manually!”

Programming is automation plain and simple.  You may have the ability to skip the manual steps and jump directly to code, but there is a manual process which is the foundation of any code you write.

It is very important to solve the problem manually first, so that you know what you are going to automate, otherwise you are just slinging code around.  Which while can be fun, will make you look like an idiot in a programming interview and will probably cause you to sweat profusely.

I recommend that you solve the problem with at least three different inputs to make sure you really understand your solution and that it will work for more than one case.

I often use a Mathematical Induction approach if possible.  Using this approach I might try and solve for 1 first, then for 2, then for n.

Also don’t forget to look for corner cases and edge cases and do any examples for those kind of cases you can think of.

It’s very important that when you solve a problem manually, you recognize what your brain is actually doing to solve the problem.  You may need to write out all the things you are normally storing in your head.  You want to be aware of each step, it is easy to gloss over them.

Let’s look at a very basic example, reversing a string.

If I give you a string “Zebra”, and ask you to reverse it, most people will do the following manual steps.

• Write “Zebra” down.
• Start a new word, and put “a” as the first letter.  (Why –> because it is the last letter, we want to start here)
• Put “r” down as the 2nd letter.  (Why –> because it is the next letter backwards from the last letter we copied)
• Put “b” down as the 3rd letter.  (Why –> same as above)

Notice how I write down each little step and why.

Optimize the manual solution

People often don’t realize how valuable this step is.  It is much easier to rearrange and reconstruct and idea or algorithm in your head than it is in code.

It’s well worth the effort to try and optimize the actual solution or simplify it when it is still in the most easily malleable state.

What you want to do here is figure out if there is another way you can solve the problem easier, or if there are some steps you can cut our or simplify.

Let’s look at our string reversal example and see if we can simplify the steps.

We should be able to immediately recognize that we can use a loop here to reduce the manual steps.  Our duplicate why’s for most of our steps tell us that we are doing the same thing over and over for each step, just with different data.

• Start at the last letter in the word and create a new empty word.
• Append the current letter to the new word
• If there is a previous letter, make the previous letter the current letter and start back at 3.

Look how close we are getting to code at this point.  You should be tempted to actually write the code for this.  That is good, it tells you that you have solved and simplified the problem well.  Writing code should now become very easy.

Write pseudo-code or comments

Many times you can skip this step if you have a really good handle on the problem or your previous steps already created a detailed enough description of the solution that coding it is already a 1 to 1 translation.

If you are a beginner or struggle with these kinds of problems, I would go ahead and take the time to do this step anyway though.

What we want to do here is capture all the steps we created and now either put them into our editor as comments or write them as psuedo-code that we can translate to real code.

By doing this, we can know exactly what the structure of the code we are going to write is going to look like which makes the job of filling in the actual code later trivial.

Let’s look at some psudeo-code for reversing a string.

// NewWord = “” // Loop backwards through word to reverse //   NewWord += CurrentLetter // Return NewWord

Pretty simple, but the key thing we have done here is outlined the structure of the code we will write to solve the problem.

Replace comments with real code

This step should be extremely easy at this point.  If you have done all the other steps, this step involves no problem solving at all.

All we do here is take each comment and convert it into a real line of code.

Taking the string reversal, we might end up with something like this.

1 for 1 translation of the comments we created above for real code.

If you struggle here, there are usually two possible reasons:

• You didn’t break down the problem into small enough steps
• You don’t know your programming language well enough to do the conversion

If you didn’t break the problem down enough, try going back to the second step and being as meticulous as possible.  Write out each and every single step.  I know it is a pain, but do it, believe me it will be worth the effort.

If you don’t know your programming language well enough to do the translation, you may need to brush up here on some basic constructs.  Any language you expect to be able to solve algorithm type problems in, you should know how to do the following things:

• Create a list
• Sort a list or array
• Create a map or dictionary
• Loop through a list, or dictionary
• Parse strings
• Convert from string to int, int to string, etc

If you don’t know how to do all of these things.  Stop what you are doing now and learn them. It’s not a very long list, and the benefits will be profound.

Optimize the real code

Sometimes this step isn’t necessary, but it’s worth taking a look at your code and figuring out if you can cut out a few lines or do something simpler.

This is also a good place to make sure all your variables are named with long meaningful names.  I cannot stress enough how important having good names for your variables and methods is for helping the person evaluating your code to understand what you were trying to do.  This is especially important when you make a mistake!

I won’t give an optimization for our trivial example of a string reversal, but a word of advice here is not to get too tricky.  Just try to mainly simplify your code and get rid of duplication.

A few final tips

If you follow this template for solving algorithm type problem, you should do very well in programming interviews, but the key to doing so is having confidence in this process.

The only way you are going to have confidence in this process is to practice it.  It takes a good amount of faith to believe that spending 70% of your 30 minutes to solve a problem just thinking about the problem and not writing any code is the right approach, so make sure you have that faith when you need it.

I’ve talked about using TopCoder to become a better programmer before, and I still recommend it.  Codility.com is another great site I have recently been introduced to.

There is one important step I did not include in the outline above, because I didn’t want to make the process any more complicated than it needed to be.

Many times you will find that a problem itself involves multiple large steps or is very complicated.  In those instances, you will want to try and find a way to cut the problem directly in half and then following the process above for each half.

This method of tackling a problem is called “divide and conquer” and is quite effective.  A good way to know where to break a problem in half is to think about what part of the problem if already given to you would make solving the rest easy.

The programming interview is merely one battle in a larger war: marketing yourself. For the full lowdown, take a look at my course: How to Market Yourself as a Software Developer .

Simple Programming Problems

Whenever I’m TA for a introductory CS class where students learn some programming language, I have trouble coming up with good exercises. Problems from Project Euler and the like are usually much too difficult for beginners, especially if they don’t have a strong background in mathematics.

This page is a collection of progressively more difficult exercises that are suitable for people who just started learning. It will be extended as I come up with new exercises. Except for the GUI questions, exercises are generally algorithmic and should be solvable without learning any libraries. The difficulty of the exercises of course somewhat depends on the programming language you use. The List exercises for example are more complicated in languages like C that don’t have build-in support for lists.

I suppose they are also useful, although much easier, whenever an experienced person wants to learn a new language.

This guide has been translated to Chinese by yifeitao Simple Programming Problems in Chinese

Before you begin

Learning to program means learning how to solve problems using code. Conceptually it is not very difficult to write a program that solves a problem that you can solve yourself. The skill you need to acquire is thinking very precisely about how you solve the problem and breaking it down into steps that are so simple that a computer can execute them. I encourage you to first solve a few instances of a problem by hand and think about what you did to find the solution. For example if the task is sorting lists, sort some short lists yourself. A reasonable method would be to find the smallest element, write it down and cross it out of the original list and repeat this process until you have sorted the whole list. Then you have to teach the computer 1) how to find the smallest element, 2) how to write it down, 3) how to cross it out, and wrap this in a loop. Then continue this task breakdown process until you’re confident you know how to write the necessary program.

To make good progress in your programming task, you need to test your work as early and as thoroughly as possible. Everybody makes mistakes while programming and finding mistakes in programs consumes a very large part of a programmer’s work-day. Finding a problem in a small and easy piece of code is much simpler than trying to spot it in a large program. This is why you should try to test each sub task you identified during your task-breakdown by itself. Only after you’re confident that each part works as you expect you can attempt to plug them together. Make sure you test the complete program as well, errors can creep in in the way the different parts interact. You should try to automate your tests. The easier it is to test your program, the freer you are in experimenting with changes.

The last important point is how you express your thoughts as code. In the same way that you can express the same argument in different ways in a normal English essay, you can express the same problem-solving method in different ways in code. Try for brevity. The lines that you don’t write are the lines where you can be sure that the don’t have bugs. Don’t be afraid to Google for idiomatic ways of doing the things you’d like to do (after you tried doing them yourself!). Remember that you don’t write the program for the computer, you write it for other humans (maybe a future you!). Choose names that explain things, add comments where these names don’t suffice. Never comment on what the code is doing, only write comments that explain why .

This is a bad example:

The exact same idea is much easier to understand if you write it like this:

Better naming and a better task breakdown make the comments obsolete. Revise your code just as you would revise an essay. Sketch, write, delete, reformulate, ask others what they think. Repeat until only the crispest possible expression of your idea remains. Revisit code you’ve written a while ago to see whether you can improve it with things you’ve learned since.

• Write a program that prints ‘Hello World’ to the screen.
• Write a program that asks the user for their name and greets them with their name.
• Modify the previous program such that only the users Alice and Bob are greeted with their names.
• Write a program that asks the user for a number n and prints the sum of the numbers 1 to n
• Modify the previous program such that only multiples of three or five are considered in the sum, e.g. 3, 5, 6, 9, 10, 12, 15 for n =17
• Write a program that asks the user for a number n and gives them the possibility to choose between computing the sum and computing the product of 1,…, n .
• Write a program that prints a multiplication table for numbers up to 12.
• Write a program that prints all prime numbers. (Note: if your programming language does not support arbitrary size numbers, printing all primes up to the largest number you can easily represent is fine too.)
• Write a guessing game where the user has to guess a secret number. After every guess the program tells the user whether their number was too large or too small. At the end the number of tries needed should be printed. It counts only as one try if they input the same number multiple times consecutively.
• Write a program that prints the next 20 leap years.
• Write a program that computes the sum of an alternating series where each element of the series is an expression of the form ( ( − 1 ) k + 1 ) / ( 2 * k − 1 ) ((-1)^{k+1})/(2 * k-1) for each value of k k from 1 to a million, multiplied by 4. Or, in more mathematical notation

4 ⋅ ∑ k = 1 10 6 ( − 1 ) k + 1 2 k − 1 = 4 ⋅ ( 1 − 1 / 3 + 1 / 5 − 1 / 7 + 1 / 9 − 1 / 11 … ) . 4\cdot \sum_{k=1}^{10^6} \frac{(-1)^{k+1}}{2k-1} = 4\cdot(1-1/3+1/5-1/7+1/9-1/11\ldots).

Lists, Strings

If your language of choice doesn’t have a build in list and/or string type (e.g. you use C), these exercises should also be solvable for arrays. However, some solutions are very different between an array-based list (like C++’s vector ) and a pointer based list (like C++’s list ), at least if you care about the efficiency of your code. So you might want to either find a library, or investigate how to implement your own linked list if your language doesn’t have it.

• Write a function that returns the largest element in a list.
• Write function that reverses a list, preferably in place.
• Write a function that checks whether an element occurs in a list.
• Write a function that returns the elements on odd positions in a list.
• Write a function that computes the running total of a list.
• Write a function that tests whether a string is a palindrome.
• Write three functions that compute the sum of the numbers in a list: using a for -loop, a while -loop and recursion. (Subject to availability of these constructs in your language of choice.)
• Write a function on_all that applies a function to every element of a list. Use it to print the first twenty perfect squares. The perfect squares can be found by multiplying each natural number with itself. The first few perfect squares are 1*1= 1 , 2*2=4 , 3*3=9 , 4*4=16 . Twelve for example is not a perfect square because there is no natural number m so that m*m=12 . (This question is tricky if your programming language makes it difficult to pass functions as arguments.)
• Write a function that concatenates two lists. [a,b,c] , [1,2,3] → [a,b,c,1,2,3]
• Write a function that combines two lists by alternatingly taking elements, e.g. [a,b,c] , [1,2,3] → [a,1,b,2,c,3] .
• Write a function that merges two sorted lists into a new sorted list. [1,4,6] , [2,3,5] → [1,2,3,4,5,6] . You can do this quicker than concatenating them followed by a sort.
• Write a function that rotates a list by k elements. For example [1,2,3,4,5,6] rotated by two becomes [3,4,5,6,1,2] . Try solving this without creating a copy of the list. How many swap or move operations do you need?
• Write a function that computes the list of the first 100 Fibonacci numbers. The first two Fibonacci numbers are 1 and 1. The n+1 -st Fibonacci number can be computed by adding the n -th and the n-1 -th Fibonacci number. The first few are therefore 1, 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8.
• Write a function that takes a number and returns a list of its digits. So for 2342 it should return [2,3,4,2] .
• Write functions that add, subtract, and multiply two numbers in their digit-list representation (and return a new digit list). If you’re ambitious you can implement Karatsuba multiplication . Try different bases . What is the best base if you care about speed? If you couldn’t completely solve the prime number exercise above due to the lack of large numbers in your language, you can now use your own library for this task.
• Write a function that takes a list of numbers, a starting base b1 and a target base b2 and interprets the list as a number in base b1 and converts it into a number in base b2 (in the form of a list-of-digits). So for example [2,1,0] in base 3 gets converted to base 10 as [2,1] .
• Implement the following sorting algorithms: Selection sort, Insertion sort, Merge sort, Quick sort, Stooge Sort. Check Wikipedia for descriptions.
• Implement binary search.

Write a function that takes a list of strings an prints them, one per line, in a rectangular frame. For example the list ["Hello", "World", "in", "a", "frame"] gets printed as:

Write function that translates a text to Pig Latin and back. English is translated to Pig Latin by taking the first letter of every word, moving it to the end of the word and adding ‘ay’. “The quick brown fox” becomes “Hetay uickqay rownbay oxfay”.

Intermediate

• Write a program that outputs all possibilities to put + or - or nothing between the numbers 1,2,…,9 (in this order) such that the result is 100. For example 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100.
• Write a program that takes the duration of a year (in fractional days) for an imaginary planet as an input and produces a leap-year rule that minimizes the difference to the planet’s solar year.
• Implement a data structure for graphs that allows modification (insertion, deletion). It should be possible to store values at edges and nodes. It might be easiest to use a dictionary of (node, edgelist) to do this.
• Write a function that generates a DOT representation of a graph.
• Using a sample text, create a directed (multi-)graph where the words of a text are nodes and there is a directed edge between u and v if u is followed by v in your sample text. Multiple occurrences lead to multiple edges.
• Do a random walk on this graph: Starting from an arbitrary node choose a random successor. If no successor exists, choose another random node.
• Write a program that automatically converts English text to Morse code and vice versa.
• Write a program that finds the longest palindromic substring of a given string. Try to be as efficient as possible!
• Think of a good interface for a list. What operations do you typically need? You might want to investigate the list interface in your language and in some other popular languages for inspiration.
• Implement your list interface using a fixed chunk of memory, say an array of size 100. If the user wants to add more stuff to your list than fits in your memory you should produce some kind of error, for example you can throw an exception if your language supports that.
• Improve your previous implementation such that an arbitrary number of elements can be stored in your list. You can for example allocate bigger and bigger chunks of memory as your list grows, copy the old elements over and release the old storage. You should probably also release this memory eventually if your list shrinks enough not to need it anymore. Think about how much bigger the new chunk of memory should be so that your performance won’t be killed by allocations. Increasing the size by 1 element for example is a bad idea.
• If you chose your growth right in the previous problem, you typically won’t allocate very often. However, adding to a big list sometimes consumes considerable time. That might be problematic in some applications. Instead try allocating new chunks of memory for new items. So when your list is full and the user wants to add something, allocate a new chunk of 100 elements instead of copying all elements over to a new large chunk. Think about where to do the book-keeping about which chunks you have. Different book keeping strategies can quite dramatically change the performance characteristics of your list.
• Implement a binary heap. Once using a list as the base data structure and once by implementing a pointer-linked binary tree. Use it for implementing heap-sort.
• Implement an unbalanced binary search tree.
• Implement a balanced binary search tree of your choice. I like (a,b)-trees best.
• Compare the performance of insertion, deletion and search on your unbalanced search tree with your balanced search tree and a sorted list. Think about good input sequences. If you implemented an (a,b)-tree, think about good values of a and b.
• Given two strings, write a program that efficiently finds the longest common subsequence.
• Given an array with numbers, write a program that efficiently answers queries of the form: “Which is the nearest larger value for the number at position i ?”, where distance is the difference in array indices. For example in the array [1,4,3,2,5,7] , the nearest larger value for 4 is 5. After linear time preprocessing you should be able to answer queries in constant time.
• Given two strings, write a program that outputs the shortest sequence of character insertions and deletions that turn one string into the other.
• Write a function that multiplies two matrices together. Make it as efficient as you can and compare the performance to a polished linear algebra library for your language. You might want to read about Strassen’s algorithm and the effects CPU caches have. Try out different matrix layouts and see what happens.
• Implement a van Emde Boas tree. Compare it with your previous search tree implementations.
• Given a set of d-dimensional rectangular boxes, write a program that computes the volume of their union. Start with 2D and work your way up.
• Write a program that displays a bouncing ball.
• Write a Memory game.
• Write a Tetris clone
• Write a program that plays Hangman as good as possible. For example you can use a large dictionary like this and select the letter that excludes most words that are still possible solutions. Try to make the program as efficient as possible, i.e. don’t scan the whole dictionary in every turn.
• Write a program that plays Rock, Paper, Scissors better than random against a human. Try to exploit that humans are very bad at generating random numbers.
• Write a program that plays Battle Ship against human opponents. It takes coordinates as input and outputs whether that was a hit or not and its own shot’s coordinates.

Other Collections

Of course I’m not the first person to come up with the idea of having a list like this.

• Several small problems Programming Practice
• CPE 101 Projects
• 99 Lisp Problems , 99 Haskell Problems . Most of these can also be done in other languages.
• Rosetta Code Programming Tasks . These come with solutions in many languages!
• Code Golf Challenges . The goal here is to solve the problem with as few characters as possible.
• SPOJ Problems . This is a list of more than 13000 Problems!
• Code Abbey According to Github user RodionGork, this is less mathy than Project Euler.

CC-BY-SA Adrian Neumann (PGP Key A0A8BC98 )

adriann.github.io

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• 19 April 2021
• 13972 views

Problem-Solving. How to Boost Your Ability to Solve Programing Tasks and Challenges

1. Make sure you understand the problem

2. break down the problem into smaller ones, 3. plan the solution first, 4. solve programming problems on various preparation platforms.

One of the most popular tech interview platforms with a huge community and over 1650 problems for you to practice. Supports 14 programming languages including Java.

Interview Cake

Another well-known website with all kinds of content for programmers, including programming tasks, articles, tips and lots of interview questions.

HackerEarth

Besides programming problems, this platform allows you to test yourself in mock interviews, as well as to participate in coding competitions and hackathons.

5. Use CodeGym to practice and learn how to approach programming problems

6. play coding games to practice problem-solving while having fun, 7. extend your knowledge of design patterns, algorithms and data structures, 8. get feedback, expert advice.

Problem Solving

Solving problems is the core of computer science. Programmers must first understand how a human solves a problem, then understand how to translate this "algorithm" into something a computer can do, and finally how to "write" the specific syntax (required by a computer) to get the job done. It is sometimes the case that a machine will solve a problem in a completely different way than a human.

Computer Programmers are problem solvers. In order to solve a problem on a computer you must:

Know how to represent the information (data) describing the problem.

Determine the steps to transform the information from one representation into another.

Information Representation

A computer, at heart, is really dumb. It can only really know about a few things... numbers, characters, booleans, and lists (called arrays) of these items. (See Data Types). Everything else must be "approximated" by combinations of these data types.

A good programmer will "encode" all the "facts" necessary to represent a problem in variables (See Variables). Further, there are "good ways" and "bad ways" to encode information. Good ways allow the computer to easily "compute" new information.

An algorithm (see Algorithm) is a set of specific steps to solve a problem. Think of it this way: if you were to tell your 3 year old neice to play your favorite song on the piano (assuming the neice has never played a piano), you would have to tell her where the piano was, and how to sit on the bench, and how to open the cover, and which keys to press, and which order to press them in, etc, etc, etc.

The core of what good programmers do is being able to define the steps necessary to accomplish a goal. Unfortunately, a computer, only knows a very restricted and limited set of possible steps. For example a computer can add two numbers. But if you want to find the average of two numbers, this is beyond the basic capabilities of a computer. To find the average, you must:

• First: Add the two numbers and save this result in a variable
• Then: Divide this new number the number two, and save this result in a variable.
• Finally: provide this number to the rest of the program (or print it for the user).

We "compute" all the time. Computing is the act of solving problems (or coming up with a plan to solve problems) in an organized manner. We don't need computers to "compute". We can use our own brain.

Encapsulation and Abstraction and Complexity Hiding

Computer scientists like to use the fancy word "Encapsulation" to show how smart we are. This is just a term for things we do as humans every day. It is combined with another fancy term: "Abstraction".

Abstraction is the idea of "ignoring the details". For example, a forest is really a vastly complex ecosystem containing trees, animals, water paths, etc, etc, etc. But to a computer scientist (and to a normal person), its just "a forest".

For example, if your professor needs a cup of coffee, and asks you the single item: "Get me a cup of coffee", he has used both encapsulation and abstraction. The number of steps required to actually get the coffee are enumerable. Including, getting up, walking down the hall, getting in your car, driving to a coffee stand, paying for the coffee, etc, etc, etc. Further, the idea of what a cup of coffee is, is abstract. Do you bring a mug of coffee, or a Styrofoam cup? Is it caffeinated or not? Is it freshly brewed or from concentrate? Does it come from Africa or America?

All of this information is TOO MUCH and we would quickly be unable to funciton if we had to remember all of these details. Thus we "abstract away" the details and only remember the few important items.

This brings us to the idea of "Complexity Hiding". Complexity hiding is the idea that most of the times details don't matter. In a computer program, as simple an idea as drawing a square on the screen involves hundreds (if not thousands) of (low level) computer instructions. Again, a person couldn't possible create interesting programs if every time they wanted to do something, they had to re-write (correctly) every one of those instructions. By "ecapsulating" what is meant by "draw square" and "reusing" this operation over and over again, we make programming tractable.

Encapsulation

The idea behind encapsulation is to store the information necessary to a particular idea in a set of variables associated with a single "object". We then create functions to manipulate this object, regardless of what the actual data is. From that point on, we treat the idea from a "high level" rather than worry about all the parts (data) and actions (functions) necessary to represent the object in a computer.

Brute Force

Brute force is a technique for solving problems that relies on a computers speed (how fast it can repeat steps) to solve a problem. For example, if you wanted to know how many times the number 8 goes into the number 100, you could do the following:

Of course this is a silly way for a computer (or a human) to solve this problem. The real way we would do it is:

When in doubt, you can often use "brute force" to solve a problem, but it often saves time (at least computer time) to think about the problem and solve it in an elegant manner.

Blog / Time To Code / 6 Ways to Improve Your Programming Problem Solving

6 Ways to Improve Your Programming Problem Solving

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Software development is, at its core, all about problem solving.

Think about it.

First, developers need to find a problem they can solve with software. Then, they have to figure out how humans solve that problem. And then, they have to find a way to effectively translate both the problem and the solution into code that a computer can use to solve the problem as well as (or better than) a person.

And then there are all the problems along the way: Working with teams, finding and fixing bugs, meeting delivery deadlines.

Engineers use problem solving skills constantly .

Because of that, if you want to become a better developer, one place to start might be becoming a better problem solver. But that’s easier said than done, and requires a deep understanding of what problem solving is, why it matters, and what it actually takes to improve those skills.

Ready to dive in? Let’s get started.

What Is Problem Solving, and Why Does It Matter?

Have you ever heard this famous Steve Jobs quote?

“Everyone in this country should learn to program a computer because it teaches you to think.”

Jobs was right. Software development is as much about “soft skills” like critical thinking, communication, and problem solving as it is about “hard skills” like writing code.

And so, in the context of software development, problem solving can mean a few different things:

• Creating an application that meets the end user’s goals.
• Communicating effectively with team members to delegate work.
• Finding and fixing bugs in the code.
• Meeting a tight deadline for a client.

There’s only one thing that’s true no matter what problem solving looks like on a given day: It’s an integral part of every step of the software development process.

Why Should Engineers Work On Problem Solving Skills?

Just like any other skill, problem solving takes practice to apply and master.

Many developers think that becoming a better problem solver means being able to solve more problems, faster. But that’s not true — it means being able to find the best solution to a problem, and then put that solution in place.

Learning to do that is a great way to become a better developer overall. And while soft skills can be more difficult to learn and improve upon than hard skills, there are still some tips and tricks that can help you get better at problem solving specifically.

6 Ways to Get Better at Problem Solving

As you’ll see from these learning tools, getting better at problem solving is mostly like getting better at any other skill for work: You need to practice. A lot. And then practice some more.

Solve a Lot of Problems on a Lot of Different Platforms

Step one? Solve as many problems as you can, but try to focus on different types of problems on different platforms.

Here’s why this is so beneficial: It prevents you from getting comfortable with one problem solving method or framework. As we already know, in the world of software development, there is definitely no one-size-fits-all solution for the problems we encounter.

When you regularly practice solving different types of problems in different platforms, it reinforces the fact that you can’t always rely on the same technique to solve every problem. It forces you to learn to be flexible, and to choose the best tool or framework for each job.

Solve Problems in Contexts Other Than Work

Since problem solving is a skill that requires practice, you can (and should) work on it even outside of work hours.

This doesn’t need to be a chore — there are a lot of fun ways to practice problem solving, like by doing math or logic puzzles, solving crosswords, or playing a game like chess. Even many video games can help work on problem solving skills.

There are also many opportunities to practice problem solving just as you live your life from day to day. Broke something around the house? Use your problem solving skills to DIY a fix. Need to solve a conflict with a friend or a family member? You guessed it — time to practice problem solving.

Learn From Past Solutions, and Apply Them to New Problems

As you keep practicing problem solving as much as possible, you’ll start to see patterns emerge in the problems you solve. You’ll build up a sort of toolkit filled with the solutions you’ve found and used in the past, and you’ll be able to apply those to solving new problems.

This part is just as important as finding the solutions in the first place, because the more you practice your growing problem solving skills, the more natural it will become to apply the right solutions to different types of problems, making you able to solve new problems more and more quickly, while still using the best possible solves.

Ask Others for Help and Feedback

Sometimes, finding the best solution to a problem just requires a fresh, new set of eyes. That’s why it’s important to treat growing your problem solving skills not as a totally solo venture, but as a team endeavor where everyone at your organization can support each other and help each other get better.

If you’re stuck on a specific problem, ask for help. Someone else might have a method or framework you aren’t familiar with, that they can teach you. You can then apply that to more problems down the road.

And if you’ve come up with a solve for a problem, ask others for feedback. They might be able to help you refine or further improve your framework, making it even better.

Train the Problem Solving Part of Your Mind

How do you keep muscles from growing weaker over time? You keep exercising them.

The same goes for your brain, and especially for different knowledge-base skills, like problem solving. You’ll stay at the top of your brain if you keep “working out,” or practicing problem solving all the time.

A good move for a developer who wants to invest in their problem solving skills is scheduling time every week (or even every day) to consciously practice problem solving. Remember, this doesn’t necessarily mean solving work problems. You could commit to doing a tricky logic puzzle every day on your lunch break, for example. The important thing is to get in the practice, no matter how that looks.

Practice Other Skills Related to Problem Solving

Problem solving is an important skill on its own. But there are other necessary skills developers need to support their problem solving abilities, and those skills all take practice, too.

Flexibility. Critical thinking. Communication. Teamwork. Focusing on building and practicing all these skills will help you improve your problem solving.

Problem solving is one of the most necessary skills for developers to have. With time, practice, and dedication, they can improve it, constantly, and keep becoming better.

Rethinking Timekeeping for Developers:

Turning a timesuck into time well spent.

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dewayne sewell

Ive learnt the skill of problem solving is like a muscle, where it is important to keep exercising it to stay strong. It is important to be aware of the soft skills necessary for effective problem solving also, such as communication, critical thinking, team working that can leverage your technical hard skills to find a solution faster/more effective. Two things I will aim to do is; 1. To solve problems on different platforms so I don’t get too comfortable on only one and stagnate. This not only challenges the brain to see things from a new perspective, but to start the habit of continuous learning and skill building. 2. Reach out to others for help / discuss problems and my solutions for feedback and advice and sharing ideas.

Pakize Bozkurt

Problem solving skills is a crucial thing to make easier or better your life. In fact as a human being we do it in every day life. I mean, we have to do it for living. There are many ways to how to do it. The best way is we should ask right questions. First of all, we should ask some questions, such as; \' Are we aware of the problem?, Are we clarify the problem? Do we go into problem rational? Do we have reasons? or Do we have evidences? Do we do check them out? etc. I am from Philosophy teacher background. I like solving problem whatever in my work or daily life. Secondly, we should have more perspectives . Although our brain is lazy, it is always in a starvation for knowledge.For this there are many enjoyable things to do it. I highly recommend to read book every day which kind of you like it and playing game or solving puzzle. I love solving Sudoku, puzzle and reading book or article. Finally, solving problem is our invatiable needed. Having flexibility, critical thinking, communication and teamwork are easy way to improve us to how we can do our work better and good life. Massive thank for this amazing article!

I read this amazing article. Normally, everyone knows that but we dont use most of time this informations. Which one is the best way to use? Really it does not matter, every one is like a gold opinion. We can use this ideas for the daily life. I have already used that learn from past solution and ask to someone who knows very well. This is so helpful for me. Sometimes google is the best option for ask to someone. Google can be the best teacher for us as well. Soft skills like a team work or solving problem and critical thinking can be important than typing code. We can learn typing code but we can not learn critical thinking and solving problems from google very well. Thank you for this article.

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Excepturi quo volupt

Thanks for this !

Fahil kiima

Thanks a lot for the ideas on problem solving,I really had a problem with that and now going to use what you\'ve informed us about to better my problem solving skills. Thanks.

Alan Codinho

Nice overview

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